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人気のある微分積分 >

integral from 0 to t of 3e^x

解

\int_{0}^{t} 3 e^{x} d x

解

3 (e^{t} - 1)

解答ステップ

\int_{0}^{t} 3 e^{x} d x

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int_{0}^{t} e^{x} d x

共通積分を使用する:

\int e^{x} d x = e^{x}

= 3 [e^{x}]_{0}^{t}

限度を計算する:

e^{t} - 1

= 3 (e^{t} - 1)

人気の例

integral from 0 to 2 of ye^{-xy}

\int_{0}^{2} y e^{- x y} d x

integral from 0 to 5 of rsqrt(25-r^2)

\int_{0}^{5} r 25 - r^{2} d r

integral from x to x^2 of (y/x)

\int_{x}^{x^{2}} (\frac{y}{x}) d y

integral from 0 to 6 of (|2x-5|)/(x+1)

\int_{0}^{6} \frac{∣ 2 x - 5 ∣}{x + 1} d x

integral from 1/2 to 2 of (2-2/(x^2))

\int_{\frac{1}{2}}^{2} (2 - \frac{2}{x ^{2}}) d x